A linear-to-linear cross-polarization converter (CPC) based on metasurface (MS) is proposed. The converter is polarization insensitive and has two wide bands. The MS is composed of periodical unit cells printed on a substrate. The top and bottom MS unit cells are formed with four groups of right-angle triangle pairs whose vertices are connected. Thus, there are eight pairs of triangles on the top and bottom surfaces of the substrate, and these pairs of triangles are arranged alternately in overlapping and orthogonal ways. The polarization conversion ratio (PCR) of the CPC is higher than 95% in the bands of 9.4 to 13.1 GHz and 13.4 to 17.2 GHz. Additionally, the PCR remains the same when the electromagnetic (EM) wave is incident at arbitrary azimuth. Furthermore, the polarization rotation angle and elliptic angle are calculated to verify the conversion effect. Finally, the conversion mechanism of the proposed converter is explored by analyzing the surface current distribution and magnetic field. The proposed converter can be applied to the field of satellite communication in Ku-band.